The earliest and most common formulation is the
`orthogonal Procrustes problem' [1]}, [2]}.
Suppose that we have two sets of measurements \(X\)  and \(Y\)  that
we know are related by an unitary (orthogonal) transformation (i.e., a rotation or reflection).
The goal is to learn the best unitary transformation that relates
the data measurements.
Thus, \(A\)  is constrained to be a unitary matrix and the minimization problem is
\(\operatornamewithlimits{arg\rm {}min}_{A^\ast A= I} \Vert Y- AX\Vert _F. &\) 
